Starsport can reveal Blues boss Antonio Conte is a huge admirer of the midfielder and has personally pinpointed him as a key target for his champions.
Oxlade-Chamberlain has just one year left on his current Gunners deal and is understood to be demanding £120,000 a week to sign a new contract, a figure they have not got anywhere near offering.
The 23-year-old is attracted by the idea of moving to Chelsea, where he can play Champions League football and looks sure to be offered the kind of money Arsenal have so far refused to pay.
The Blues initially offered £25m - the same as Liverpool were willing to pay - but have now raised that figure in the light of Conte becoming angry about the lack of transfer activity at Stamford Bridge this summer.
Oxlade-Chamberlain was forced to play wing back at times last season after Arsene Wenger switched to a 3-4-3 formation.
But he remains adamant that midfield remains his favoured position.
Starsport revealed previously how Wenger is adamant none of his star players will be allowed to go to a title rival, even if they are in the last year of their contracts.
Yesterday he raved about Oxlade-Chamberlain, who joined the Gunners from Southampton for £12m six years ago.
“Personally, I think he is a hugely talented player,” said Wenger. “He is on the way up and he will continue to move up because that potential is there.
“He is today very conscious of his qualities as well, which he was not always, and I personally believe he will be a very great player.”
Wenger confirmed star striker Alexis Sanchez will miss tomorrow’s opening Premier League game at home to Leicester along with the clash at Stoke eight days later.
He said the Chile star, who is also in the last year of his contract and been heavily linked with a move to Manchester City, suffered an abdominal muscle strain in training before Sunday’s Community Shield win over Chelsea.
A scan failed to show up any damage with Wenger admitting the injury is a “little” one.
Meanwhile, Wenger has warned goalkeeper Petr Cech he is not guaranteed the No.1 role at Arsenal this season.
Wenger persuaded Chile international David Ospina to stay this summer and said: “They are top-level players, they want to go to the World Cup.
“But Ospina will get a number of games here and he will fight with Cech.
“The fight is quite open. At the moment I play Cech but this battle is not won definitely by Cech because I rate Ospina highly.”
